Write True or False and justify your answer.
The cost of levelling the ground in the form of a triangle having the sides $51 \, m$,$37 \, m$,and $20 \, m$ at the rate of $Rs \, 3$ per $m^2$ is $Rs \, 918$.

(TRUE) The sides of the triangle are $a = 51 \, m$,$b = 37 \, m$,and $c = 20 \, m$.
The semi-perimeter $s$ is calculated as:
$s = \frac{a + b + c}{2} = \frac{51 + 37 + 20}{2} = \frac{108}{2} = 54 \, m$.
Using Heron's formula,the area of the triangle is:
$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$
$= \sqrt{54(54-51)(54-37)(54-20)}$
$= \sqrt{54 \times 3 \times 17 \times 34}$
$= \sqrt{(2 \times 3^3) \times 3 \times 17 \times (2 \times 17)}$
$= \sqrt{2^2 \times 3^4 \times 17^2} = 2 \times 3^2 \times 17 = 2 \times 9 \times 17 = 306 \, m^2$.
The cost of levelling the ground is $\text{Area} \times \text{Rate} = 306 \, m^2 \times Rs \, 3/m^2 = Rs \, 918$.
Since the calculated cost matches the given value,the statement is True.